Digital to Analog Converters Alexander Gurney Alexander Pitt Gautam Puri 1.
Transcript of Digital to Analog Converters Alexander Gurney Alexander Pitt Gautam Puri 1.
Digital to Analog Converters
Alexander GurneyAlexander PittGautam Puri
1
Digital to Analog Converters Alexander Gurney What is a DAC?
Applications of DACs
Alexander Pitt Types of DACsBinary Weighted ResistorR-2R Ladder
Gautam Puri SpecificationsResolutionSpeedLinearitySettling TimeReference VoltagesErrors
2
What is a DAC? A DAC converts a binary digital signal into an
analog representation of the same signal Typically the analog signal is a voltage output,
though current output can also be used
0101
0011
0111
1001
1001
1010
1011 DAC
What is a DAC? – Alexander Gurney
3
Reference Voltage
DACs rely on an input Reference Voltage to calculate the Output Signal
What is a DAC? – Alexander Gurney
4
Binary to Analog Conversion
1011100110100111 10000110010101000011001000010000Digital Input Signal
Ana
log
Out
put
Sig
nal
Each sample is converted from binary to analog, between 0 and Vref for Unipolar, or Vref and –Vref for Bipolar
What is a DAC? – Alexander Gurney
5
Sampling Frequency Sampling frequency is the number of data
points sampled per unit time Sampling frequency must be twice the
frequency of the sampled signal to avoid aliasing, per Nyquist criteria
A higher sampling frequency decreases the sampling period, allowing more data to be transmitted in the same amount of time
What is a DAC? – Alexander Gurney
6
Output is a Piecewise Function This is due to finite sampling frequency The analog value is calculated and “held” over
the sampling period This results in an imperfect reconstruction of
the original signal
Ideally Sampled Signal Output typical of a real, practical DAC due to sample & hold
DAC
What is a DAC? – Alexander Gurney
7
An Example
4 Bit signal Unipolar Vref = 7V 8 Sample Points Sample Frequency = 1 hertz Duration 8 seconds
0001 0011 0110 1100 1011 0101 0010 0111
What is a DAC? – Alexander Gurney
8
Filtering
The analog signal generated by the DAC can be smoothed using a low pass filter
This removes the high frequencies required to sustain the sharp inclines making up the edges
0 bit
nth bit
n bit DAC011010010101010100101101010101011111100101000010101010111110011010101010101010101010111010101011110011000100101010101010001111
Digital Input
Filter
Piece-wise Continuous Output
Analog Continuous Output
What is a DAC? – Alexander Gurney
9
DACs in Audio
Digital AnalogMP3s ->3.5mm Audio OutHD Radio ->Signal received by speakerCDs ->RCA Audio Out
What is a DAC? – Alexander Gurney
10
DACs in Video
Digital AnalogDVDs ->Composite OutputOTA Broadcast ->Converter Box OutputYoutube ->Analog Monitor Input
What is a DAC? – Alexander Gurney
11
Types of Digital to Analog Converters
Binary Weighted Explanation Advantages and disadvantages
R-2R Ladder Explanation Example Advantages and disadvantages
DAC Types – Alex Pitt
12
Binary Weighted DAC
Use transistors to switch between open and close
Use a summing op-amp circuit with gain
Adds resistors in parallel scaled by two to divide voltage on each branch by a power of two
DAC Types – Alex Pitt
13
Vout =
Analog Out
Binary Weighted DAC
Circuit can be simplified by adding resistors in parallel to substitute for Rin. *Values for A, B, C and D are either 1 or 0.
DAC Types – Alex Pitt
14
Binary Weighted DAC
R
B
R
B
R
B
R
BRV
R
RVV nnn
inin 1-n0321
fin
fout 242
MSB LSB
General equation B0 B1 B2 B3
DAC Types – Alex Pitt
15
Binary Weighted DAC
Advantages Works well up to ~ 8-bit conversions
Disadvantages Needs large range of resistor values (2048:1 for
a 12-bit DAC) with high precision resistor values
Too much or too little current flowing through resistors Minimum/maximum opamp current Noise overwhelms current through larger resistance
values
DAC Types – Alex Pitt
16
R-2R Ladder DAC
Requires only two resistance values (R and 2R)
Vref
4 bit converter
Each bit controls a switch between ground and the inverting input of the op amp.
The switch is connected to ground if the corresponding bit is zero.
DAC Types – Alex Pitt
17
RF
R-2R Ladder Example
Convert 0001 to analog
V0V1V2V3
0 1 11
2
RV V V
R R
V1
1 2 21
2
RV V V
R R
2 3 31
2
RV V V
R R
Vref
V0
DAC Types – Alex Pitt
18
1
1/ 2 1/ 2eqR RR R
RF
R-2R Ladder Example
19
Convert 0001 to analog
01
8 refV V
2RR
V0
out 0R 1
V2R 16 refV V
Vref
DAC Types – Alex Pitt
RF
RF
R
Rf
R-2R Ladder
By adding resistance in series and in parallel we can derive an equation for the R-2R ladder.
DAC Types – Alex Pitt
20
R-2R Ladder
By knowing how current flows through the ladder we can come up with a general equation for R-2R DACs.
MSB
LSB
DAC Types – Alex Pitt
21
f0123
fout 16842R
BBBBIRIV sum
R-2R Ladder
Rf
1
out ref0 2
nf i
n ii
R BV V
R
f0123
fout 16842R
BBBB
R
VRIV ref
sum
4-Bit Equation Substituting
General Equation
DAC Types – Alex Pitt
22
R
VI ref
R-2R Ladder DAC
Advantages Only two resistor values Can use lower precision resistors
DAC Types – Alex Pitt
23
Specifications of DACLets discuss some terms you’ll hear when dealing with DACs
Reference Voltage Resolution Speed Linearity Settling Time Some types of Errors
Specifications - Gautam Puri
24
Reference Voltage Vref
The reference voltage determines the range of output voltages from the DAC
For a ‘Non-Multiplying DAC’, Vref is a constant value set internally by the manufacturer
For a ‘Multiplying DAC’, Vref is set externally and can be varied during operation
Vref also affects DAC resolution (which will be discussed later).
Specifications - Gautam Puri
25
Full scale voltage Full scale voltage is the output voltage when all
the bits of the digital input signal are 1s.
It is slightly less than reference voltage Vref
Vfs = Vref - VLSB
N
NVV
2
)12(reffs
Specifications - Gautam Puri
26
Resolution of a DAC is the change in output voltage for a change in the least significant bit (LSB) of the digital input
Resolution is specified in “bits”. Most DACs have a resolution of 8 to 16 bits
Example: A DAC with 10 bits has a resolution of
Higher resolution (more bits) = smoother output A DAC with 8 bits has 256 steps whereas one with 16 bits
has 65536 steps for the given voltage range and can thus offer smoother output
Resolution
LSBref
2Resolution V
VN
ref10ref
1024
1
2Resolution V
V
Specifications - Gautam Puri
27
Speed (Sampling frequency) Sampling frequency is the rate at which the DAC
accepts digital input and produces voltage output In order to avoid aliasing, the Nyquist criterion
requires that
Sampling frequency is limited by the input clock speed (depends on microcontroller) and the settling time of the DAC
maxsampling 2 ff
Specifications - Gautam Puri
28
Settling Time
It takes the DAC a finite amount of time to produce the exact analog voltage corresponding to the digital input
The settling time is the time interval from when the DAC commands the update of its output to when the voltage actually reaches ± ½ VLSB.
A faster DAC will have a smaller settling time
tsettle
Specifications - Gautam Puri
29
Linearity If the change in analog output voltage per unit
change in digital input remains constant over the entire range of operation, the DAC is said to be linear
Ideally the DAC should have a proportionality constant which results in a linear slope
Non-linearity is considered an error, and will be further discussed in the errors section
010101000011001000010000Digital Input Signal
Ana
log
Out
put S
igna
l
010101000011001000010000 010101000011001000010000Digital Input Signal
Ana
log
Out
put S
igna
l
010101000011001000010000Digital Input Signal
Ana
log
Out
put S
igna
l
010101000011001000010000 010101000011001000010000Digital Input Signal
Ana
log
Out
put S
igna
l
Linear Non-linear
Specifications - Gautam Puri
30
Types of DAC Errors Non-monotonic output error Non-linear output error
― Differential― Integral
Gain error Offset error Full scale error Resolution error Settling time and overshoot error
Specifications - Gautam Puri
31
Non-monotonic Output Error A monotonic function has a slope whose sign does not
change Non-monotonic error results when the analog output
changes direction for a step or a few steps of digital input In a closed loop control system this may cause the DAC to
toggle continuously between 2 input codes and the system will be unstable.
Specifications - Gautam Puri
32
Differential non-linear output error For a change in the LSB of input, the output of an
ideal DAC is VLSB
However in a non-linear DAC the output may not be exactly the LSB but rather a fraction (higher or lower) of it
Specifications - Gautam Puri
33
Differential non-linear output error Basically “differential” non-linearity expresses the
error in step size as a fraction of LSB The DNL is the maximum of these deviations over
the entire transfer function One must choose a DAC with DNL less than 1 LSB.
A DNL > 1 LSB will lead to non-monotonic behavior. This means that for certain steps in digital input, the output voltage will change in the opposite direction. This may cause a closed loop control system to become unstable as the system may end up oscillating back and forth between two points.
Specifications - Gautam Puri
34
Integral non-linear output error The integral non-linearity error is the difference
between the ideal and actual output. It can also be defined as the difference between ideal and a best fit line
INL occurs when the output is non-linear and thus unable to adhere to a straight line.
The maximum deviation from this line is called INL.
Specifications - Gautam Puri
35
Integral non-linear output error INL is expressed as fraction of LSB. INL cannot be calibrated out as the non-
linearity is unpredictable and one does not know where the maximum deviation from the ideal line will occur.
One must choose an ADC with an INL (maximum deviation) within the accuracy required.
Specifications - Gautam Puri
36
More important - DNL or INL ?
The DNL and INL are both important non-linear errors to be aware of.
In the case of an application such as an imaging one, where slight differences in color densities are important, the “differential” non-linearity error is more important.
In an application where the parameters vary more widely, such as speed of a vehicle, the “integral” non-linearity error may be of greater importance
Specifications - Gautam Puri
37
Gain Error The difference between the output voltage (or
current) with full scale input code and theideal voltage (or current) that should exist with a full scale input code2 Types of Gain Error 1. Low Gain: Step
Amplitude Less than Ideal
2. High Gain: Step Amplitude Greater than Ideal
Gain Error can be adjusted to zero by using an external potentiometer
Specifications - Gautam Puri
38
Offset Error It is the difference in ideal and actual output voltage at a
digital input of zero All output values will differ from the ideal values by that
same amount, hence the output is “offset” from the input Offset can be ‘positive’ or ‘negative’ It can be fixed by adding/subtracting the difference to the
digital input before passing through the DAC
Specifications - Gautam Puri
39
Full Scale Error It is a combination of gain and offset error It is measured at the full scale input
Specifications - Gautam Puri
40
Resolution Error If the resolution is not high enough, the DAC
cannot accurately output the required waveform Lower resolution results in higher resolution error
Low resolution (1 bit) Higher resolution (3 bits)
Specifications - Gautam Puri
41
Settling Time and Overshoot Error If settling time is too high, the DAC will not
produce the ideal output waveform fast enough and there will be a delay or lag.
This will also lower the maximum operating frequency of the DAC.
Specifications - Gautam Puri
42
References• Previous semester lecture slides• http://www.hitequest.com/Hardware/a_dac.ht
m http://www.national.com/appinfo/adc/files/ms101157.pdf
• http://www.noise.physx.u-szeged.hu/DigitalMeasurements/ADConversion/ADSpecs.pdf
• Scherz, Paul. Practical Electronics for Inventors. 2nd Edition, McGraw Hill. 2007.
• http://masteringelectronicsdesign.com/an-adc-and-dac-differential-non-linearity-dnl/
• http://masteringelectronicsdesign.com/an-adc-and-dac-integral-non-linearity-inl/
43
Questions ?
Alexander Gurney
What is a DAC?
Alexander Pitt
Types of DACs
Guatam Puri
Specifications
44